Back-propagation algorithm [1]} and gradient descent is used in neural networks to update Weights and biases. Parameters in trainable activation functions are updated using the same technique. The forward pass is implemented in both Pytorch [2]} & Tensorflow-Keras [3]} API, and automatic differentiation will update the parameters. Alternatively, CUDA [4]} based implementation (see [5]}) can be used and the gradients of equation (3) for the input \(x\)  and the parameter \(\alpha \)  can be computed as follows:
\(\frac{\partial G}{\partial x} = \frac{-n^2x}{2n}\sqrt{\frac{2}{\pi }}e^{\frac{-n^2x^2}{2}}+\frac{(1+\alpha )}{2}+\frac{(1-\alpha )}{2} \ \operatorname{erf}\left(\frac{nx}{\sqrt{2}}\right)+\frac{n(1-\alpha )}{\sqrt{2\pi }} \ x \ e^{-{\frac{n^2x^2}{2}}}\) 
\(\frac{\partial G}{\partial \alpha } = \frac{x}{2}\left(1 - \operatorname{erf}\left(\frac{nx}{\sqrt{2}}\right)\right).\) 
